Sums of Independent Random Variables
The classical large-sample theory is about the sum of independent random variables. Even though large-sample techniques have expanded well beyond the classical theory, the foundation set up by the latter remains the best way to understand and further explore elements of large-sample theory. Furthermore, the classical results are often used as examples to illustrate more sophisticated theory, as we have done repeatedly so far in this book, and the “gold standard“ for any extensions beyond the classical situation. Here, by gold standard it means that a well-developed, nonclassical large-sample theory should include the classical one as a special case.
KeywordsConvergence Rate Central Limit Theorem Independent Random Variable Invariance Principle Iterate Logarithm
Unable to display preview. Download preview PDF.